Integrated edge and junction detection with the boundary tensor

The boundaries of image regions necessarily consist of edges (in particular, step and roof edges), corners, and junctions. Currently, different algorithms are used to detect each boundary type separately, but the integration of the results into a single boundary representation is difficult. Therefore, a method for the simultaneous detection of all boundary types is needed. We propose to combine responses of suitable polar separable filters into what we will call the boundary tensor. The trace of this tensor is a measure of boundary strength, while the small eigenvalue and its difference to the large one represent corner/junction and edge strengths respectively. We prove that the edge strength measure behaves like a rotationally invariant quadrature filter. A number of examples demonstrate the properties of the new method and illustrate its application to image segmentation.